(p,q) unshuffle

Let p and q be positive natural numbers. Further, let S(k) be the symmetric groupMathworldPlanetmathPlanetmath on the numbers {1,,k}. A permutationMathworldPlanetmath τS(p+q) is a (p,q) unshuffle if there exist i1<<ip and j1<<jq s.t.




Alternatively a (p,q) unshuffle is a permutation τS(p+q) s.t. τ-1 is a (p,q) shuffle.

Since a (p,q) unshuffle is completely determined by {i1,,ip}, the cardinality of {σS(p+q)|σ is an unshuffle} is (p+qq).

Title (p,q) unshuffle
Canonical name pqUnshuffle
Date of creation 2013-03-22 16:47:45
Last modified on 2013-03-22 16:47:45
Owner Karid (16341)
Last modified by Karid (16341)
Numerical id 10
Author Karid (16341)
Entry type Definition
Classification msc 20B99
Classification msc 05A05